Download Type Theory and Formal Proof: An Introduction, by Rob Nederpelt, Herman Geuvers
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Type Theory and Formal Proof: An Introduction, by Rob Nederpelt, Herman Geuvers
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Type theory is a fast-evolving field at the crossroads of logic, computer science and mathematics. This gentle step-by-step introduction is ideal for graduate students and researchers who need to understand the ins and outs of the mathematical machinery, the role of logical rules therein, the essential contribution of definitions and the decisive nature of well-structured proofs. The authors begin with untyped lambda calculus and proceed to several fundamental type systems, including the well-known and powerful Calculus of Constructions. The book also covers the essence of proof checking and proof development, and the use of dependent type theory to formalise mathematics. The only prerequisite is a basic knowledge of undergraduate mathematics. Carefully chosen examples illustrate the theory throughout. Each chapter ends with a summary of the content, some historical context, suggestions for further reading and a selection of exercises to help readers familiarise themselves with the material.
- Sales Rank: #646382 in Books
- Published on: 2014-12-15
- Original language: English
- Number of items: 1
- Dimensions: 9.72" h x .98" w x 6.85" l, 2.14 pounds
- Binding: Hardcover
- 466 pages
About the Author
Rob Nederpelt was Lecturer in Logic for Computer Science until his retirement. Currently he is a guest researcher in the Faculty of Mathematics and Computer Science at Eindhoven University of Technology, The Netherlands.
Herman Geuvers is Professor in Theoretical Informatics at the Radboud University Nijmegen, and Professor in Proving with Computer Assistance at Eindhoven University of Technology, both in The Netherlands.
Most helpful customer reviews
5 of 6 people found the following review helpful.
Outstanding but for the RIGHT audience...
By Let's Compare Options Preptorial
This is a unique and outstanding book for the right audience. And therein lieth the rub. I am using it as an introduction for Software Engineers in an online course on Category Theory (CT), even though CT is not even mentioned in the index. By giving rigorous coverage of types from untyped Lambda calc all the way through Barendregt's - lambda cubes, the reader is totally immersed in the machinery of the construction of proof assistants.
The publisher states that this is a great intro, and only requires undergrad math. Maybe undergrad math, senior year, at MIT, with half a dozen courses in set theory, analysis, and formal proof systems? Can we be honest-- today in the US you can get your PhD in math without taking a single set theory course, let alone Category Theory! And, just like you can drive a car without knowing how it works, even as an advanced software designer, you can use proof assistant software without having the foggiest about underlying mappings and translations between, say, number theory and lambda calculus. That said, EVERYONE who has read this book in my classes, even those who only got 30% of it, say to a person that it made them better thinkers, more intuitive and gave them a MUCH deeper understanding of how computational mathematics and software proof systems work. I mean, just the discussion of assumptions vs. axioms and primitives taken as definitions sets off light bulbs at the PhD level about what variables, constants and parameters really are.
Look up Besout's little theorem on Wiki. You will see the elegant way that the applied tool of using synthetic division and remainders can more efficiently perform polynomial division than long division itself. The theorem is used an a deep exercise and example of proof formalization, mechanization, efficient code, proven correctness etc. work together, giving not only the underpinnings of proof assistants, but also seeing the practical side (from a computational complexity/ efficiency point of view) of typing.
Highly recommended for the right audience, but not for the faint at heart. VERY well written, as it does not use the usual, highly abstract terse, PROBLEM/ PROBLEM/ THEORY/ PROOF/ EXAMPLE/ EXAMPLE... now it's your turn technique. Instead outstanding (though British) English is used to flesh out the details of what and why techniques are being used in each toolbox. This will need to be studied deeply to get to 30% if you are new to lambda, type or category theories, some of the most abstract topics in math/computing, but the reward is immense, not just in those fields, but in making us better understand the workings of human logic, proof, evidence and clear thinking.
0 of 3 people found the following review helpful.
Very useful.
By He Shen
Very well presented. Very well designed exercises. Very useful.
0 of 3 people found the following review helpful.
Highly recommended.
By B. Paulewicz
It is a pleasure to read - the authors clearly have a deep understanding of the issues involved and are enthusiastic about the subject. Highly recommended.
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